In marine geophysical data acquisition, measurements may be taken of wavefields that have been initiated by geophysical energy sources such as air guns, marine vibrators, electric bipole antennae, and magnetic coils. The geophysical energy sources may be positioned at known locations in a geographic area. In a marine setting, the sources may be towed behind one or more boats traveling a prescribed course, usually a group of aligned paths. The geophysical sources are caused to emit energy. For example, when the geophysical source is a seismic source, sonic pulses are emitted, and sensors record reflected sonic waves as voltages from transducers. The data received may be compiled into a data set with time and distance along and across the sampling paths. Such data is commonly used to prospect for geologic resources such as oil and gas deposits.
The data set obtained typically contains information of interest indicating the geology of earth strata below the geophysical equipment. Unfortunately, however, the geologic information is usually obscured by substantial noise from a wide variety of sources. Coherent noise sources, such as hydrostatic pressure variations, cavitation of boat propellers, and seismic interference, are usually well-defined and easily removed. Incoherent noise sources, however, such as tugging noise caused by sudden movements of a vessel or sensor due to wave motion, strumming or vibration of cables, and swell noise, are more difficult to remove.
Conventional methods of processing the data set include performing integral transform operations, such as Fourier transforms and/or Radon transforms, on the data set. Such operations may lead to mathematical incompatibilities. For example, Fourier transforms are defined for functions or data with domain of infinite extent, whereas recorded data is only available in a domain of finite extent. Prior to performing a Fourier transform on recorded data, an extrapolation is typically applied at the edges of the domain of the data set to smooth the edges numerically. These operations frequently produce spectral artefacts in the data. There is a need to remove such artefacts.
To facilitate understanding, identical reference numerals have been used, where possible, to designate identical elements that are common to the figures. It is contemplated that elements disclosed in one embodiment may be beneficially utilized on other embodiments without specific recitation.